"Greece is more popular this year than we've seen it in many years," saidDamian McCabe, CEO of McCabe World Travel. "This has a lot to do with the strength of the U.S. dollar and also no visible political strife. Press or news about the impending financial crisis has not stopped travelers from asking about travel to Greece this summer."

Travel and tourism are expected to account for 9.5 percent of total Greek employment in 2015, according to a recent report by the World Travel and Tourism Council.

The travel search website Kayak said Greece remains a popular destination. "Athens was named one of our top trending destinations in 2015. We've seen a 17 percent increase in searches to Athens year over year," said Dave Solomito, North America brand director at Kayak.

Greece could see social unrest, regardless of whether the country exits the euro zone. Athens has seen peaceful protests this week.

"There could be unrest if the there is no agreement or if the agreement doesn't sit well with the Greeks. Social unrest is not conducive to tourism," said Mauro Guillen, economics professor and director of the the Lauder Institute at the Wharton School of the University of Pennsylvania.

Yannis Behrakis | Reuters

Pro-European Union protesters scuffle with riot police outside the parliament building during a rally in Athens, June 22, 2015.

On the other hand, a possible exit from the euro zone would mean a severely weakened currency—whether it's the euro or a revived drachma. This would bode well for tourists hailing from countries with stronger currencies.

Elena Frangakis-Syrett, a professor at Queens College who researches and has published on Greece, said the purchasing power of U.S. tourists would increase in the event of significant monetary policy changes.

But she thinks an exit from the common European currency area is unlikely. "Even if there is political strife, [it] can be contained to protests, rallies et cetera, as it has been the case so far," she said.

CORRECTION: This article was updated to correct a quote by Mauro Guillen, economics professor and director of the the Lauder Institute at the Wharton School of the University of Pennsylvania, who said, "Social unrest is not conducive to tourism."